Question

Find the variance and standard deviation for the data:57,64, 43, 67, 49, 59, 44, 47, 61, 59

Answer 1

Given observations are 57, 64, 43, 67, 49, 59, 44, 47, 61, 59
The sum of these observations is 550
The number of observations is 10
The mean of the given observations is 55
i.e Mean= Sum of observations/Number of observations= 550/10= 55
Let the mean be A
 x            x-A       (x-A)²
57            2            4
64            9           81
43          -12         144
67           12         144
49           -6          36
59            4           16
44          -11          121
47           -8          64
61            6           36
59           4           16
Σ(x-A)² =662
Variance(s²)= [Σ(x-A)²]/(n-1)= 662/9= 73.556
Standard deviation(s)= √variance =√s² = 8.576
Hope it helps.